Refraction at Plane Surfaces: NEB Class 11 Physics Guide

Curriculum boundary

What plane-surface refraction includes

The CDC secondary curriculum includes laws of refraction and lateral shift. Check the CDC Physics Grade 11 page for current Nepal resources.

This guide follows OpenStax Snell’s law, plane-interface apparent depth and the critical-angle treatment.

Physical meaning

Speed, index and wave direction

Absolute refractive index n=c/v compares light speed in vacuum with phase speed in a medium. A larger n means lower speed. Frequency stays fixed at a stationary boundary because the wave must match in time; wavelength changes according to v=fλ.

Refraction is the change of propagation direction when speed changes across a boundary. At normal incidence θ=0, speed and wavelength change but the ray does not bend. Angles are always measured from the normal, not the surface.

Law of refraction

Use Snell’s law with a direction prediction

n₁sinθ₁=n₂sinθ₂. Draw the boundary and normal, label the incident medium first, and predict whether θ₂ is smaller or larger. An inverse-sine result outside 0–1 signals impossible transmission for that assumed geometry.

Image by a plane interface

Real depth and apparent depth

Rays from an underwater object refract away from the normal into air. The eye traces them backward in straight lines, so the object appears shallower. For near-normal viewing, n_{object medium}/n_{observer medium}≈real depth/apparent depth.

The simple ratio is a paraxial small-angle approximation. At large viewing angles, use ray geometry with Snell’s law rather than treating apparent depth as a single universal point.

Parallel faces

Lateral displacement through a glass slab

At the first face the ray bends toward the normal; at the parallel second face it bends away. Because the outer media are the same and faces parallel, the emergent ray is parallel to the incident ray but laterally displaced.

For slab thickness t, incidence i and refraction r, the standard shift is d=t sin(i−r)/cos r. The displacement is zero at normal incidence, grows with thickness and usually grows with incidence angle.

Transmission limit

Critical angle and total internal reflection

Total internal reflection requires travel from higher n₁ to lower n₂ and incidence greater than the critical angle. At critical incidence the refracted ray has θ₂=90°, so sinθ_c=n₂/n₁.

There is no critical-angle condition for light going from lower to higher index. At θ below critical, some light is transmitted and some reflected.

Context and applications

Where plane refraction appears

Practical method

Measure refractive index of a block

Trace the block, send a narrow ray at several incident angles, mark incident and emergent paths, remove the block and join points. Draw normals and measure i and r. Plot sin i against sin r; for air-to-block, gradient approximates block index.

Use a ray box or teacher-approved low-power source; never look into a beam. Narrow lines, careful pin alignment, no block movement and a large angle range reduce uncertainty. A best-fit line is stronger than averaging individual ratios.

Use PhET Bending Light after predicting the ray.

Exam routine

Seven steps for plane refraction

1. Draw boundary and normal.
2. Label incident and refracted media.
3. Predict toward or away from normal.
4. Measure angles from the normal.
5. Apply Snell’s law or the correct geometry relation.
6. Check sine range, units and limiting cases.
7. State paraxial or plane-parallel assumptions.

Review curved-mirror ray practice for construction habits and Physical Quantities for unit checks. For online or physical NEB tuition, call 9846662070.

Practice tasks

Closed-book checkpoint

1. Define refractive index.
2. Predict bending for four boundaries.
3. Solve three Snell-law questions.
4. Derive near-normal apparent depth.
5. Calculate a slab shift.
6. Find a critical angle.
7. Explain TIR conditions.
8. Evaluate a sin i–sin r experiment.

References and next steps

Sources and related study guides

• CDC Nepal: Physics Grade 11
• CDC Nepal: Secondary Curriculum
• OpenStax: Law of Refraction
• OpenStax: Apparent Depth
• OpenStax: Total Internal Reflection
• OpenStax: Optics Questions
• PhET: Bending Light

Continue with the plane-surface refraction study guide. Curriculum scope and sources were checked on 2 August 2026; follow current CDC, NEB and college instructions if requirements change.

Wave connection

What stays continuous at the boundary

The frequency is fixed by the source and remains the same across a stationary interface. Since v=fλ, a lower wave speed in the higher-index medium means a shorter wavelength. The change in direction follows from the wavefront matching condition expressed by Snell’s law.

This connection prevents the false claim that refraction occurs because frequency changes. It also explains why refractive index can depend on wavelength, leading to prism dispersion later.

Multiple boundaries

Track rays through layers without losing medium order

For parallel layers, apply Snell’s law at each interface using the ray angle and indices on that specific boundary. A ray entering glass from air bends toward the normal, entering water from glass may bend away if water has lower n, and finally entering air bends farther away. Frequency stays common across all stationary interfaces.

When all boundaries are parallel and the first and final media are the same, the final emergent direction can be parallel to the incident direction, though the path is displaced. Non-parallel faces, as in a prism, create net angular deviation.

Critical-angle reasoning in a fibre

A higher-index core surrounded by lower-index cladding can guide rays that meet the core boundary above the critical angle. Real fibres also involve entry acceptance, bending loss, dispersion and material attenuation; total internal reflection is the central geometric-optics model, not the entire communication system.

Approximation limit

Why apparent depth depends on viewing geometry

The simple depth ratio follows from small angles where sinθ≈tanθ. At an oblique view, different rays from the object can back-project to positions that do not collapse into the same near-normal image point. Use Snell’s law and triangle geometry for the stated observer position.

A written solution should therefore say “viewed nearly normally” before applying real depth/apparent depth. This small phrase protects the model boundary and explains why a photograph from the side may show a different apparent shift.